New and sophisticated biomarkers for the early detection and prevention of chronic and acute diseases are constantly being developed in laboratory settings. Receiver Operating Characteristics (ROC) curves are used in biomedical research to evaluate the effectiveness of biomarkers in distinguishing individuals with and without a disease. The area under the ROC curve is the most commonly used overall measure of diagnostic tests' effectiveness There is substantial literature on statistical inference on the area under the ROC curve under various assumptions on the distributions of the measurements from healthy and disease subjects. We focus our research on ROC methodology development; especially in the following problems: 1.In the context of high cost assays, analyzing the results based on a smaller number of pooled specimens has been found to be useful. We developed design methods and statistical tools to evaluate these biomarkers. We will expand our research in this area, especially we will evaluate the estimation of the optimal cut point under pooled samples and also the robustness of the assumptions we have made in our previous work. 2.In the diagnosis of diseases, it has become more common for the diagnostic test to be performed on multiple samples that come from the same patient. There are several sources of correlation in such settings. We consider the design and analysis issues of such studies under normality assumption. We are expanding these methods to a nonparametric setting. 3.We also consider combining multiple biomarkers to improve diagnostic accuracy. Su and Liu (1993) derived the linear combinations that maximize the area under the receiver operating characteristic (ROC) curve. These linear combinations, however, may have low sensitivity for high specificity. We further investigate the performance of Su and Liu's (1993) linear combination and seek alternatives that perform well on high specificity. 4.Further developments in ROC research are underway such as sequential evaluation of biomarkers for the early detection of diseases. 5.Many biomarkers data is subject to selection bias. Referral bias is the most common type of selection bias in screening tests data. We developed methods to correct for referral bias for the area under the ROC curve.